We extend the ultraspherical spectral method to solving nonlinear ordinary differential
equation (ODE) boundary value problems. Naive ultraspherical Newton implementations …

We introduce a method to numerically compute equilibrium measures for problems with
attractive-repulsive power law kernels of the form $ K (xy)=\frac {| xy|^\alpha}{\alpha}-\frac …

This paper introduces a new numerical technique based on the implicit spectral collocation
method and the fractional Chelyshkov basis functions for solving the fractional Fredholm …

We have developed a method for constructing spectral approximations for convolution
operators of Fredholm type. The algorithm we propose is numerically stable and takes …

We present a sparse spectral method for nonlinear integro-differential Volterra equations
based on the Volterra operator's banded sparsity structure when acting on specific Jacobi …

We introduce and analyze a sparse spectral method for the solution of Volterra integral
equations using bivariate orthogonal polynomials on a triangle domain. The sparsity of the …

We discuss a method which provides accurate numerical solutions to fractional-in-time
partial differential equations posed on [0, T]× Ω with Ω⊂ R d without the excessive memory …

This paper presents an efficient spectral method for solving the fractional Fredholm integro-
differential equations. The non-smoothness of the solutions to such problems leads to the …

It is a very challenging task to solve a nonlinear integral equation in multidimensions. The
main purpose of this paper is to develop and analyze a spectral collocation method for a …

The main purpose of this work was to develop a spectrally accurate collocation method for
solving nonlinear fractional Fredholm integro-differential equations (non-FFIDEs). A …